Abstract

The problem of endowing preferences with manifold structures emerged
from discussions with Gerard Debreu in 1975 . Time has shown that such
structures can be useful in understanding the behavior of economic systems .

In Chichilnisky (1976) spaces of smooth preferences were endowed with a
Hilbert manifold structure, and this was used to study the existence and
structural stability of competitive equilibria in economies where preferences
might be non-monotonic and non-convex . This paper constructs manifolds of
preferences and applies this construction to the aggregation of preferences . We
examine the topological complexity of manifolds of smooth preferences and
use this to determine when appropriate aggregation rules exist and when they
do not .